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Simplifying (4r + 7)(7r + 4) = 0 Reorder the terms: (7 + 4r)(7r + 4) = 0 Reorder the terms: (7 + 4r)(4 + 7r) = 0 Multiply (7 + 4r) * (4 + 7r) (7(4 + 7r) + 4r * (4 + 7r)) = 0 ((4 * 7 + 7r * 7) + 4r * (4 + 7r)) = 0 ((28 + 49r) + 4r * (4 + 7r)) = 0 (28 + 49r + (4 * 4r + 7r * 4r)) = 0 (28 + 49r + (16r + 28r2)) = 0 Combine like terms: 49r + 16r = 65r (28 + 65r + 28r2) = 0 Solving 28 + 65r + 28r2 = 0 Solving for variable 'r'. Factor a trinomial. (7 + 4r)(4 + 7r) = 0Subproblem 1
Set the factor '(7 + 4r)' equal to zero and attempt to solve: Simplifying 7 + 4r = 0 Solving 7 + 4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4r = 0 + -7 4r = 0 + -7 Combine like terms: 0 + -7 = -7 4r = -7 Divide each side by '4'. r = -1.75 Simplifying r = -1.75Subproblem 2
Set the factor '(4 + 7r)' equal to zero and attempt to solve: Simplifying 4 + 7r = 0 Solving 4 + 7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7r = 0 + -4 7r = 0 + -4 Combine like terms: 0 + -4 = -4 7r = -4 Divide each side by '7'. r = -0.5714285714 Simplifying r = -0.5714285714Solution
r = {-1.75, -0.5714285714}
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